Clean stone cladding

I put up some stone cladding the other day.

I had to cut small pieces to finish it off along the ceiling so it was difficult to keep tiles clean.

There was a little tile cement got on the front of some of them here and there.

I thought it would come off with a brush and water after but that has caused a sort of chalky residue left on it that's hard to remove.

Is there something I can put on it to help me remove it?

It's stubborn enough, especially in a few joints.